Mathematical Sciences: Singular Perturbations in Applied Mathematics: Methods and Applications

本研究将发展并应用新的奇异摄动方法求解非线性常微分方程和偏积分-微分-差分方程的边值问题。结果将使我们能够计算波动的平稳分布，以及受噪声影响的动力系统从（确定性）稳定状态的转变率。随机积分-微分-差分方程及其相关的前向和后向Kolmogorov方程也将进行分析。这项研究将直接应用于科学和工程领域的各种问题。其中包括计算机性能评估、客户服务队列安排、化学物理、动力系统稳定构型之间的噪声诱导转换等。

This research will develop and apply new singular perturbation methods to boundary value problems for nonlinear ordinary differential equations and for partial integro-differential-difference equations. The results will enable us to calculate the stationary distribution of fluctuations about, and the rate of transitions from (deterministically) stable states of dynamical systems subject to noise. Stochastic integro-differential-difference equations and their associated forward and backward Kolmogorov equations will also be analyzed. The research will have direct applications to a variety of problems in science and engineering. Among them are computer performance evaluation, customer service queue arrangements, chemical physics, noise induced transitions between stable configurations of a dynamical system, etc.